Mean Posterior Estimate (MPE) of a "GaussianInvWishart" object

Description

Generate the MPE estimate of Sigma in following model structure:

x \sim Gaussian(mu,Sigma)

Sigma \sim InvWishart(v,S)

mu is known. Gaussian() is the Gaussian distribution. See ?dGaussian and ?dInvWishart for the definition of the distributions.
The model structure and prior parameters are stored in a "GaussianInvWishart" object.
The MPE estimates are:

• (Sigma_MPE) = E(Sigma|v,S,x,mu)

Usage

## S3 method for class 'GaussianInvWishart'
MPE(obj, ...)

Arguments

Value

matrix, the MPE estimate of "Sigma".

References

Gelman, Andrew, et al. Bayesian data analysis. CRC press, 2013.

MARolA, K. V., JT KBNT, and J. M. Bibly. Multivariate analysis. AcadeInic Press, Londres, 1979.

See Also

GaussianInvWishart

Examples

obj <- GaussianInvWishart(gamma=list(mu=c(-1.5,1.5),v=3,S=diag(2)))
x <- rGaussian(100,mu = c(-1.5,1.5),Sigma = matrix(c(0.1,0.03,0.03,0.1),2,2))
ss <- sufficientStatistics(obj=obj,x=x,foreach = FALSE)
posterior(obj=obj,ss = ss)
MPE(obj)